I am gong through this now. Here's where I'm at:
Nexus 4: Best there is, but not available on Verizon.
Droid DNA: Flat awesome phone. Downsides: No expandable memory (no SD card, etc), and no removable battery.
Samsung Galaxy S3: Flat awesome phone. Downsides: Superseded by Galaxy S4 (but now costs MUCH less).
If you don't need the latest and greatest, the S3 is a fantastic phone andhas a great bang for the buck right now.
Galaxy S4: The best out there right now. But you'll pay for it.
Droid Razr Maxx HD: I have the Droid Razr Maxx (not HD) and love it. Loads and loads of battery life. It's not quad core and whatnot, but phones have just about reached the point of declining returns where PCs are, where doubling the number of cores opens an app .1 seconds faster... Big deal.
If you CANNOT have a dead battery, the Razr Maxx is the only choice.
IPhone 4s: Cheap now, but no LTE.
IPhone 5: LTE, but don't underestimate the PITA factor of the switch from 30 pin to Lightning connector. Proprietary, they have a chip embedded that can prevent 3rd party accessories from working right.
I got an IPad Mini, realized just how mad this was going to be, and returned it for an IPad 3 (full size) and a Nexus 7.
PS - Have you tried wiping, doing a factory reset, and restoring the Droid X? I had a Droid (and an IPhone) that I thought were dying. A complete reset and restore and they were good as new.